I would like to pick out small objects from a category. I would like to find such a notion which

Dream 1. Picks out the schemes of finite type over $k$ from the category of $k$-schemes. Or at least picks out something relevant.

Dream 2. Picks out the top spaces homotopic to finite CW-complexes from the category of topological spaces (equipped with the Quillen model structure). (or something relevant)

Question: What notions exist for "small" objects (other than the compact objects)?

References or comments are welcomed.:) Thanks!